Simplify the following expression: $r = \dfrac{40y}{-16y^2 - 4y}$ You can assume $y \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $40y = (2\cdot2\cdot2\cdot5 \cdot y)$ The denominator can be factored: $-16y^2 - 4y = - (2\cdot2\cdot2\cdot2 \cdot y \cdot y) - (2\cdot2 \cdot y)$ The greatest common factor of all the terms is $4y$ Factoring out $4y$ gives us: $r = \dfrac{(4y)(10)}{(4y)(-4y - 1)}$ Dividing both the numerator and denominator by $4y$ gives: $r = \dfrac{10}{-4y - 1}$